Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9122617778\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 5 x^{15} - 43 x^{14} + 234 x^{13} + 634 x^{12} - 4048 x^{11} - 3483 x^{10} + 32512 x^{9} + \cdots - 208 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(4.02229\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.02229 | 1.79882 | 0.899411 | − | 0.437104i | \(-0.143996\pi\) | ||||
0.899411 | + | 0.437104i | \(0.143996\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.04331 | 1.52823 | 0.764114 | − | 0.645081i | \(-0.223177\pi\) | ||||
0.764114 | + | 0.645081i | \(0.223177\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.42405 | −1.03239 | −0.516195 | − | 0.856471i | \(-0.672652\pi\) | ||||
−0.516195 | + | 0.856471i | \(0.672652\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.92009 | 1.36459 | 0.682294 | − | 0.731078i | \(-0.260982\pi\) | ||||
0.682294 | + | 0.731078i | \(0.260982\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.02229 | −1.03855 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.60807 | 1.11762 | 0.558810 | − | 0.829295i | \(-0.311258\pi\) | ||||
0.558810 | + | 0.829295i | \(0.311258\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.63146 | 1.75078 | 0.875388 | − | 0.483421i | \(-0.160606\pi\) | ||||
0.875388 | + | 0.483421i | \(0.160606\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.04331 | −0.882323 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.1788 | 2.23576 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.21724 | −0.757438 | −0.378719 | − | 0.925512i | \(-0.623635\pi\) | ||||
−0.378719 | + | 0.925512i | \(0.623635\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.42405 | 0.596050 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 16.2634 | 2.74901 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.25376 | 0.534915 | 0.267458 | − | 0.963570i | \(-0.413816\pi\) | ||||
0.267458 | + | 0.963570i | \(0.413816\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.92009 | −0.787845 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.81231 | −0.595383 | −0.297692 | − | 0.954662i | \(-0.596217\pi\) | ||||
−0.297692 | + | 0.954662i | \(0.596217\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.87928 | −0.744083 | −0.372041 | − | 0.928216i | \(-0.621342\pi\) | ||||
−0.372041 | + | 0.928216i | \(0.621342\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.02229 | 0.599607 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.28191 | 0.624581 | 0.312290 | − | 0.949987i | \(-0.398904\pi\) | ||||
0.312290 | + | 0.949987i | \(0.398904\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.34836 | 1.33548 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.60807 | −0.645259 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.5936 | 1.59251 | 0.796253 | − | 0.604964i | \(-0.206812\pi\) | ||||
0.796253 | + | 0.604964i | \(0.206812\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.7725 | −1.85709 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.63146 | −1.01081 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.70683 | 0.612777 | 0.306389 | − | 0.951907i | \(-0.400879\pi\) | ||||
0.306389 | + | 0.951907i | \(0.400879\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.5681 | −1.35311 | −0.676554 | − | 0.736393i | \(-0.736527\pi\) | ||||
−0.676554 | + | 0.736393i | \(0.736527\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.04331 | 0.509409 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 19.7900 | 2.45465 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.2771 | −1.86639 | −0.933197 | − | 0.359365i | \(-0.882993\pi\) | ||||
−0.933197 | + | 0.359365i | \(0.882993\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.01655 | −0.832711 | −0.416356 | − | 0.909202i | \(-0.636693\pi\) | ||||
−0.416356 | + | 0.909202i | \(0.636693\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.3905 | −1.33316 | −0.666580 | − | 0.745434i | \(-0.732242\pi\) | ||||
−0.666580 | + | 0.745434i | \(0.732242\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.1788 | −1.29082 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.8445 | −1.57773 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.09508 | −0.573241 | −0.286621 | − | 0.958044i | \(-0.592532\pi\) | ||||
−0.286621 | + | 0.958044i | \(0.592532\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.476321 | −0.0522830 | −0.0261415 | − | 0.999658i | \(-0.508322\pi\) | ||||
−0.0261415 | + | 0.999658i | \(0.508322\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.5350 | 2.01040 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.93310 | 0.946907 | 0.473453 | − | 0.880819i | \(-0.343007\pi\) | ||||
0.473453 | + | 0.880819i | \(0.343007\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.8935 | 2.08540 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.21724 | 0.437307 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 30.6959 | 3.14934 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.9323 | 1.51615 | 0.758075 | − | 0.652168i | \(-0.226140\pi\) | ||||
0.758075 | + | 0.652168i | \(0.226140\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.42405 | −0.344130 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.2354 | −1.01847 | −0.509233 | − | 0.860629i | \(-0.670071\pi\) | ||||
−0.509233 | + | 0.860629i | \(0.670071\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.1878 | −1.10237 | −0.551183 | − | 0.834384i | \(-0.685823\pi\) | ||||
−0.551183 | + | 0.834384i | \(0.685823\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −16.2634 | −1.58714 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.6748 | 1.51534 | 0.757671 | − | 0.652637i | \(-0.226337\pi\) | ||||
0.757671 | + | 0.652637i | \(0.226337\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.3071 | −1.56194 | −0.780968 | − | 0.624572i | \(-0.785274\pi\) | ||||
−0.780968 | + | 0.624572i | \(0.785274\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.25376 | −0.308833 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.1546 | 1.42562 | 0.712812 | − | 0.701355i | \(-0.247421\pi\) | ||||
0.712812 | + | 0.701355i | \(0.247421\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.02229 | 0.375080 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.92009 | 0.454863 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.6319 | 1.70798 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.724108 | 0.0658280 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.81231 | 0.343745 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 24.8529 | 2.22291 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.7464 | −1.75221 | −0.876104 | − | 0.482123i | \(-0.839866\pi\) | ||||
−0.876104 | + | 0.482123i | \(0.839866\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.87928 | 0.429597 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.99863 | 0.174621 | 0.0873107 | − | 0.996181i | \(-0.472173\pi\) | ||||
0.0873107 | + | 0.996181i | \(0.472173\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 30.8564 | 2.67559 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.02229 | −0.346183 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.85067 | −0.328985 | −0.164492 | − | 0.986378i | \(-0.552599\pi\) | ||||
−0.164492 | + | 0.986378i | \(0.552599\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.64898 | 0.479140 | 0.239570 | − | 0.970879i | \(-0.422993\pi\) | ||||
0.239570 | + | 0.970879i | \(0.422993\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.28191 | −0.360602 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.8466 | −1.40879 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.02229 | 0.334033 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.34836 | −0.771040 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.9170 | −1.22205 | −0.611023 | − | 0.791613i | \(-0.709242\pi\) | ||||
−0.611023 | + | 0.791613i | \(0.709242\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.91177 | −0.481093 | −0.240547 | − | 0.970638i | \(-0.577327\pi\) | ||||
−0.240547 | + | 0.970638i | \(0.577327\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.60807 | 0.372540 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.9629 | −1.36250 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.9191 | −1.35029 | −0.675146 | − | 0.737684i | \(-0.735920\pi\) | ||||
−0.675146 | + | 0.737684i | \(0.735920\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.5936 | −0.919434 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.04331 | 0.318658 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0575 | 0.944412 | 0.472206 | − | 0.881488i | \(-0.343458\pi\) | ||||
0.472206 | + | 0.881488i | \(0.343458\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.7725 | 1.07219 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.41234 | −0.650966 | −0.325483 | − | 0.945548i | \(-0.605527\pi\) | ||||
−0.325483 | + | 0.945548i | \(0.605527\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.2073 | 0.862101 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.63146 | 0.583592 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.2440 | −1.53913 | −0.769563 | − | 0.638571i | \(-0.779526\pi\) | ||||
−0.769563 | + | 0.638571i | \(0.779526\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 45.1994 | 3.41675 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.70683 | −0.353787 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.01898 | 0.524623 | 0.262312 | − | 0.964983i | \(-0.415515\pi\) | ||||
0.262312 | + | 0.964983i | \(0.415515\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.5088 | −1.00410 | −0.502050 | − | 0.864838i | \(-0.667421\pi\) | ||||
−0.502050 | + | 0.864838i | \(0.667421\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.5681 | 0.781217 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.0876 | 0.962217 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.7783 | −1.15382 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.04331 | −0.294108 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.6319 | −1.05872 | −0.529362 | − | 0.848396i | \(-0.677569\pi\) | ||||
−0.529362 | + | 0.848396i | \(0.677569\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.90206 | −0.424840 | −0.212420 | − | 0.977178i | \(-0.568134\pi\) | ||||
−0.212420 | + | 0.977178i | \(0.568134\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −19.7900 | −1.41719 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.58043 | 0.255095 | 0.127548 | − | 0.991832i | \(-0.459289\pi\) | ||||
0.127548 | + | 0.991832i | \(0.459289\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.206157 | −0.0146141 | −0.00730703 | − | 0.999973i | \(-0.502326\pi\) | ||||
−0.00730703 | + | 0.999973i | \(0.502326\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.2771 | 1.07756 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.04331 | 0.283785 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.3342 | −1.07099 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −26.1305 | −1.80748 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.7071 | −1.83860 | −0.919298 | − | 0.393563i | \(-0.871242\pi\) | ||||
−0.919298 | + | 0.393563i | \(0.871242\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.01655 | 0.480766 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.6259 | −1.33847 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.0516 | −1.15754 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.3905 | 0.769700 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.6721 | 1.52509 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.90704 | 0.462529 | 0.231265 | − | 0.972891i | \(-0.425714\pi\) | ||||
0.231265 | + | 0.972891i | \(0.425714\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.1788 | 0.745254 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.0517430 | −0.00343430 | −0.00171715 | − | 0.999999i | \(-0.500547\pi\) | ||||
−0.00171715 | + | 0.999999i | \(0.500547\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.67060 | 0.242560 | 0.121280 | − | 0.992618i | \(-0.461300\pi\) | ||||
0.121280 | + | 0.992618i | \(0.461300\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.8445 | 0.910901 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.6446 | 1.22145 | 0.610723 | − | 0.791844i | \(-0.290879\pi\) | ||||
0.610723 | + | 0.791844i | \(0.290879\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.2231 | 1.12351 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.09508 | 0.330961 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.1647 | −1.11029 | −0.555147 | − | 0.831752i | \(-0.687338\pi\) | ||||
−0.555147 | + | 0.831752i | \(0.687338\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.5050 | −0.998762 | −0.499381 | − | 0.866383i | \(-0.666439\pi\) | ||||
−0.499381 | + | 0.866383i | \(0.666439\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 37.6018 | 2.40229 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 37.5475 | 2.38909 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.476321 | 0.0301856 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.04662 | −0.129181 | −0.0645907 | − | 0.997912i | \(-0.520574\pi\) | ||||
−0.0645907 | + | 0.997912i | \(0.520574\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.42405 | −0.215268 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −18.5350 | −1.16071 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.5277 | 1.59238 | 0.796188 | − | 0.605049i | \(-0.206847\pi\) | ||||
0.796188 | + | 0.605049i | \(0.206847\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.1560 | 0.817472 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.2098 | −0.999539 | −0.499770 | − | 0.866158i | \(-0.666582\pi\) | ||||
−0.499770 | + | 0.866158i | \(0.666582\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 46.6329 | 2.86464 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.93310 | −0.546697 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.0182 | −0.976646 | −0.488323 | − | 0.872663i | \(-0.662391\pi\) | ||||
−0.488323 | + | 0.872663i | \(0.662391\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.64736 | −0.221561 | −0.110781 | − | 0.993845i | \(-0.535335\pi\) | ||||
−0.110781 | + | 0.993845i | \(0.535335\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −19.8935 | −1.20401 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −38.2768 | −2.30818 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.19668 | −0.492491 | −0.246245 | − | 0.969208i | \(-0.579197\pi\) | ||||
−0.246245 | + | 0.969208i | \(0.579197\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.21724 | −0.252479 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.6032 | −1.82563 | −0.912817 | − | 0.408368i | \(-0.866098\pi\) | ||||
−0.912817 | + | 0.408368i | \(0.866098\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.1893 | −1.08124 | −0.540622 | − | 0.841266i | \(-0.681811\pi\) | ||||
−0.540622 | + | 0.841266i | \(0.681811\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −30.6959 | −1.81827 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.4144 | −0.909881 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.23430 | 0.249077 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.9323 | −0.875349 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.5008 | 1.48977 | 0.744887 | − | 0.667191i | \(-0.232503\pi\) | ||||
0.744887 | + | 0.667191i | \(0.232503\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.9322 | 1.10228 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.42405 | 0.198683 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.92009 | 0.284536 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.7284 | −1.13713 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.2354 | 0.588011 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −42.5080 | −2.43400 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.49238 | 0.370540 | 0.185270 | − | 0.982688i | \(-0.440684\pi\) | ||||
0.185270 | + | 0.982688i | \(0.440684\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.1878 | 0.636451 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.0601 | −1.76126 | −0.880630 | − | 0.473805i | \(-0.842880\pi\) | ||||
−0.880630 | + | 0.473805i | \(0.842880\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.1142 | 1.19344 | 0.596722 | − | 0.802448i | \(-0.296470\pi\) | ||||
0.596722 | + | 0.802448i | \(0.296470\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 16.2634 | 0.916337 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.5266 | 0.815897 | 0.407948 | − | 0.913005i | \(-0.366244\pi\) | ||||
0.407948 | + | 0.913005i | \(0.366244\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.42405 | −0.191710 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.6748 | −0.874883 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 35.1663 | 1.95670 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 55.0008 | 3.05089 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.3071 | 0.901784 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.3131 | 0.954502 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.6417 | −0.969678 | −0.484839 | − | 0.874603i | \(-0.661122\pi\) | ||||
−0.484839 | + | 0.874603i | \(0.661122\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.25376 | 0.178305 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −61.4489 | −3.35731 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.7050 | −1.01893 | −0.509464 | − | 0.860492i | \(-0.670156\pi\) | ||||
−0.509464 | + | 0.860492i | \(0.670156\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.1546 | −0.823085 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.4400 | 0.781971 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.49516 | 0.512690 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.02229 | −0.216553 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.6707 | −1.27071 | −0.635355 | − | 0.772220i | \(-0.719146\pi\) | ||||
−0.635355 | + | 0.772220i | \(0.719146\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.5123 | −1.09800 | −0.548999 | − | 0.835823i | \(-0.684991\pi\) | ||||
−0.548999 | + | 0.835823i | \(0.684991\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.92009 | −0.262615 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.8808 | 1.80329 | 0.901646 | − | 0.432475i | \(-0.142360\pi\) | ||||
0.901646 | + | 0.432475i | \(0.142360\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −28.2226 | −1.49790 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18.6319 | −0.986102 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.37177 | 0.283511 | 0.141755 | − | 0.989902i | \(-0.454725\pi\) | ||||
0.141755 | + | 0.989902i | \(0.454725\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.2391 | 2.06522 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.724108 | −0.0380058 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −45.8160 | −2.39812 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.2226 | −1.21221 | −0.606106 | − | 0.795384i | \(-0.707269\pi\) | ||||
−0.606106 | + | 0.795384i | \(0.707269\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.81231 | −0.198461 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 46.8766 | 2.43371 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 37.2210 | 1.92723 | 0.963615 | − | 0.267293i | \(-0.0861290\pi\) | ||||
0.963615 | + | 0.267293i | \(0.0861290\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −24.8529 | −1.28340 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.92009 | 0.253398 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.5601 | 1.56977 | 0.784884 | − | 0.619643i | \(-0.212723\pi\) | ||||
0.784884 | + | 0.619643i | \(0.212723\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.7464 | 1.01164 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.5302 | 1.30453 | 0.652266 | − | 0.757990i | \(-0.273818\pi\) | ||||
0.652266 | + | 0.757990i | \(0.273818\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −55.6865 | −2.83805 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.87928 | −0.248028 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.3878 | −1.54072 | −0.770362 | − | 0.637606i | \(-0.779925\pi\) | ||||
−0.770362 | + | 0.637606i | \(0.779925\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.60807 | 0.233040 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.99863 | −0.100818 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.4939 | −1.03116 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.14774 | 0.157981 | 0.0789903 | − | 0.996875i | \(-0.474830\pi\) | ||||
0.0789903 | + | 0.996875i | \(0.474830\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −30.8564 | −1.54475 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.83957 | −0.391489 | −0.195745 | − | 0.980655i | \(-0.562712\pi\) | ||||
−0.195745 | + | 0.980655i | \(0.562712\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.7492 | −1.03359 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.02229 | 0.199869 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.1410 | −0.552241 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.94580 | −0.244554 | −0.122277 | − | 0.992496i | \(-0.539020\pi\) | ||||
−0.122277 | + | 0.992496i | \(0.539020\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.85067 | 0.189939 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.0312 | 0.936463 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.91590 | −0.0940478 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.64898 | −0.276632 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.0781 | 1.02973 | 0.514867 | − | 0.857270i | \(-0.327841\pi\) | ||||
0.514867 | + | 0.857270i | \(0.327841\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.5556 | −0.904343 | −0.452172 | − | 0.891931i | \(-0.649351\pi\) | ||||
−0.452172 | + | 0.891931i | \(0.649351\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.28191 | 0.208194 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 51.5127 | 2.49873 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −42.7301 | −2.06786 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.8466 | 0.813363 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.248683 | −0.0119786 | −0.00598931 | − | 0.999982i | \(-0.501906\pi\) | ||||
−0.00598931 | + | 0.999982i | \(0.501906\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.8676 | −1.53146 | −0.765731 | − | 0.643161i | \(-0.777622\pi\) | ||||
−0.765731 | + | 0.643161i | \(0.777622\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.02229 | −0.192854 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.63146 | 0.365062 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.1853 | 0.820208 | 0.410104 | − | 0.912039i | \(-0.365492\pi\) | ||||
0.410104 | + | 0.912039i | \(0.365492\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.34836 | 0.445160 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.7251 | 1.26975 | 0.634875 | − | 0.772615i | \(-0.281052\pi\) | ||||
0.634875 | + | 0.772615i | \(0.281052\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 35.9315 | 1.70332 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.9170 | 0.705548 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.0993 | 1.18451 | 0.592254 | − | 0.805751i | \(-0.298238\pi\) | ||||
0.592254 | + | 0.805751i | \(0.298238\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.0535 | 0.614667 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.91177 | 0.277759 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 80.0173 | 3.75127 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.68062 | 0.218950 | 0.109475 | − | 0.993990i | \(-0.465083\pi\) | ||||
0.109475 | + | 0.993990i | \(0.465083\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.60807 | −0.215086 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.78731 | −0.409266 | −0.204633 | − | 0.978839i | \(-0.565600\pi\) | ||||
−0.204633 | + | 0.978839i | \(0.565600\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.6797 | 1.47228 | 0.736139 | − | 0.676830i | \(-0.236647\pi\) | ||||
0.736139 | + | 0.676830i | \(0.236647\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.9629 | 0.786637 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.0114 | 0.787196 | 0.393598 | − | 0.919283i | \(-0.371230\pi\) | ||||
0.393598 | + | 0.919283i | \(0.371230\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −61.7701 | −2.85228 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.9191 | 0.779592 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.7069 | 0.768183 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 85.3106 | 3.91432 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.5936 | 0.530835 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.3153 | 1.29376 | 0.646880 | − | 0.762592i | \(-0.276073\pi\) | ||||
0.646880 | + | 0.762592i | \(0.276073\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0088 | 0.729939 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.04331 | −0.183977 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 60.0622 | 2.72728 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.5510 | 0.885942 | 0.442971 | − | 0.896536i | \(-0.353925\pi\) | ||||
0.442971 | + | 0.896536i | \(0.353925\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.0575 | −0.545257 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.8233 | −1.39103 | −0.695517 | − | 0.718510i | \(-0.744825\pi\) | ||||
−0.695517 | + | 0.718510i | \(0.744825\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.60807 | 0.207537 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.7725 | −0.619028 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −28.3701 | −1.27257 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.3081 | −1.44631 | −0.723154 | − | 0.690687i | \(-0.757308\pi\) | ||||
−0.723154 | + | 0.690687i | \(0.757308\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.41234 | 0.375836 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.6976 | −0.967449 | −0.483725 | − | 0.875220i | \(-0.660716\pi\) | ||||
−0.483725 | + | 0.875220i | \(0.660716\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −41.1699 | −1.83204 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.2073 | −0.497734 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.16165 | −0.273110 | −0.136555 | − | 0.990632i | \(-0.543603\pi\) | ||||
−0.136555 | + | 0.990632i | \(0.543603\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −46.0554 | −2.03737 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.63146 | −0.336937 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −45.0005 | −1.98296 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.6615 | −0.644810 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.2440 | 0.888615 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.32842 | −0.364875 | −0.182437 | − | 0.983217i | \(-0.558399\pi\) | ||||
−0.182437 | + | 0.983217i | \(0.558399\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.4234 | 0.586965 | 0.293482 | − | 0.955964i | \(-0.405186\pi\) | ||||
0.293482 | + | 0.955964i | \(0.405186\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −45.1994 | −1.97266 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.4333 | −0.846528 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.70683 | 0.204259 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.7569 | −0.812453 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 63.0486 | 2.72583 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.01898 | −0.302892 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −32.0092 | −1.37874 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.0066 | −0.860153 | −0.430076 | − | 0.902792i | \(-0.641513\pi\) | ||||
−0.430076 | + | 0.902792i | \(0.641513\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.5088 | 0.579718 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −65.5918 | −2.80964 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.1367 | 1.24580 | 0.622898 | − | 0.782303i | \(-0.285955\pi\) | ||||
0.622898 | + | 0.782303i | \(0.285955\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.5681 | −0.451036 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.63146 | 0.325111 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.6010 | −0.876043 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.0876 | −0.555536 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.2619 | 1.53646 | 0.768232 | − | 0.640171i | \(-0.221137\pi\) | ||||
0.768232 | + | 0.640171i | \(0.221137\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.0065 | −1.01537 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.7783 | 0.666158 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.3050 | 0.982190 | 0.491095 | − | 0.871106i | \(-0.336597\pi\) | ||||
0.491095 | + | 0.871106i | \(0.336597\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 60.9562 | 2.56444 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.04331 | 0.169803 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.6105 | −0.696350 | −0.348175 | − | 0.937430i | \(-0.613198\pi\) | ||||
−0.348175 | + | 0.937430i | \(0.613198\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.2191 | 0.762444 | 0.381222 | − | 0.924483i | \(-0.375503\pi\) | ||||
0.381222 | + | 0.924483i | \(0.375503\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.6319 | 0.611254 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.1788 | 0.466188 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.5487 | 1.10524 | 0.552619 | − | 0.833434i | \(-0.313628\pi\) | ||||
0.552619 | + | 0.833434i | \(0.313628\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.90206 | 0.245281 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.92591 | −0.0799003 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −39.6971 | −1.64409 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.7900 | 0.818217 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.48638 | −0.267722 | −0.133861 | − | 0.991000i | \(-0.542738\pi\) | ||||
−0.133861 | + | 0.991000i | \(0.542738\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.1837 | −1.32610 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.58043 | −0.147279 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.2027 | 1.52773 | 0.763866 | − | 0.645375i | \(-0.223299\pi\) | ||||
0.763866 | + | 0.645375i | \(0.223299\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 74.9427 | 3.07235 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.206157 | 0.00843744 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −47.8509 | −1.95514 | −0.977568 | − | 0.210618i | \(-0.932452\pi\) | ||||
−0.977568 | + | 0.210618i | \(0.932452\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.4176 | 0.751270 | 0.375635 | − | 0.926768i | \(-0.377425\pi\) | ||||
0.375635 | + | 0.926768i | \(0.377425\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.2771 | −0.622131 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.91257 | 0.118413 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.4814 | 0.668959 | 0.334480 | − | 0.942403i | \(-0.391439\pi\) | ||||
0.334480 | + | 0.942403i | \(0.391439\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.04331 | −0.163843 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.0674 | 0.852295 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.2142 | −0.776056 | −0.388028 | − | 0.921648i | \(-0.626844\pi\) | ||||
−0.388028 | + | 0.921648i | \(0.626844\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.3342 | 0.618336 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.92586 | −0.238566 | −0.119283 | − | 0.992860i | \(-0.538060\pi\) | ||||
−0.119283 | + | 0.992860i | \(0.538060\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.0096 | 1.72870 | 0.864351 | − | 0.502889i | \(-0.167729\pi\) | ||||
0.864351 | + | 0.502889i | \(0.167729\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 36.1193 | 1.44709 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 44.0717 | 1.76287 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 26.1305 | 1.04355 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.9936 | 0.597832 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.8343 | −1.18769 | −0.593843 | − | 0.804581i | \(-0.702390\pi\) | ||||
−0.593843 | + | 0.804581i | \(0.702390\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 26.7071 | 1.06151 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −79.4256 | −3.15191 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 45.9948 | 1.82238 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.01655 | −0.277570 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.1137 | 1.34741 | 0.673705 | − | 0.739000i | \(-0.264702\pi\) | ||||
0.673705 | + | 0.739000i | \(0.264702\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.9368 | 1.06229 | 0.531143 | − | 0.847282i | \(-0.321763\pi\) | ||||
0.531143 | + | 0.847282i | \(0.321763\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.6259 | 0.772768 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.38305 | 0.133001 | 0.0665006 | − | 0.997786i | \(-0.478817\pi\) | ||||
0.0665006 | + | 0.997786i | \(0.478817\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.1164 | −0.632625 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.0516 | 0.668305 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.1857 | 0.789929 | 0.394964 | − | 0.918696i | \(-0.370757\pi\) | ||||
0.394964 | + | 0.918696i | \(0.370757\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.03908 | 0.314113 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.3905 | −0.444386 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.3517 | 0.714881 | 0.357441 | − | 0.933936i | \(-0.383649\pi\) | ||||
0.357441 | + | 0.933936i | \(0.383649\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.7589 | 1.15749 | 0.578744 | − | 0.815509i | \(-0.303543\pi\) | ||||
0.578744 | + | 0.815509i | \(0.303543\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22.6721 | −0.880513 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 124.113 | 4.81290 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.90704 | −0.267041 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.1857 | 1.39693 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.25389 | −0.202523 | −0.101261 | − | 0.994860i | \(-0.532288\pi\) | ||||
−0.101261 | + | 0.994860i | \(0.532288\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11.1788 | −0.430272 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.9045 | 1.34149 | 0.670745 | − | 0.741688i | \(-0.265975\pi\) | ||||
0.670745 | + | 0.741688i | \(0.265975\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 60.3761 | 2.31702 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0517430 | 0.00198280 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.35781 | −0.358067 | −0.179033 | − | 0.983843i | \(-0.557297\pi\) | ||||
−0.179033 | + | 0.983843i | \(0.557297\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.4885 | −0.591785 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.67060 | −0.140042 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 57.0417 | 2.17312 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.96336 | 0.188815 | 0.0944076 | − | 0.995534i | \(-0.469904\pi\) | ||||
0.0944076 | + | 0.995534i | \(0.469904\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.8445 | −0.525909 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.7218 | 0.861888 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.5674 | −0.665413 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.6446 | −0.705202 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.6860 | 0.705762 | 0.352881 | − | 0.935668i | \(-0.385202\pi\) | ||||
0.352881 | + | 0.935668i | \(0.385202\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.8309 | 0.936517 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.2231 | −0.648659 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −41.3851 | −1.55645 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.8457 | 1.27110 | 0.635551 | − | 0.772059i | \(-0.280773\pi\) | ||||
0.635551 | + | 0.772059i | \(0.280773\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.09508 | −0.191080 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.21724 | −0.157937 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −67.7620 | −2.53416 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17.1647 | 0.641029 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.94275 | 0.370802 | 0.185401 | − | 0.982663i | \(-0.440642\pi\) | ||||
0.185401 | + | 0.982663i | \(0.440642\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −45.2357 | −1.68467 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.5050 | 0.576635 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.1788 | 0.415170 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.49962 | −0.203970 | −0.101985 | − | 0.994786i | \(-0.532519\pi\) | ||||
−0.101985 | + | 0.994786i | \(0.532519\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.4841 | −0.831603 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.7108 | 1.31901 | 0.659504 | − | 0.751701i | \(-0.270766\pi\) | ||||
0.659504 | + | 0.751701i | \(0.270766\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −37.6018 | −1.38696 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 52.3095 | 1.92685 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.9990 | 1.50817 | 0.754087 | − | 0.656775i | \(-0.228080\pi\) | ||||
0.754087 | + | 0.656775i | \(0.228080\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −37.5475 | −1.37934 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.54115 | −0.129912 | −0.0649562 | − | 0.997888i | \(-0.520691\pi\) | ||||
−0.0649562 | + | 0.997888i | \(0.520691\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −60.0004 | −2.19824 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.476321 | −0.0174277 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 63.3782 | 2.31579 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.915056 | 0.0333909 | 0.0166954 | − | 0.999861i | \(-0.494685\pi\) | ||||
0.0166954 | + | 0.999861i | \(0.494685\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.04662 | 0.0745829 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23.7789 | −0.865401 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.75926 | 0.100287 | 0.0501435 | − | 0.998742i | \(-0.484032\pi\) | ||||
0.0501435 | + | 0.998742i | \(0.484032\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.42405 | 0.124285 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.4124 | −0.848698 | −0.424349 | − | 0.905499i | \(-0.639497\pi\) | ||||
−0.424349 | + | 0.905499i | \(0.639497\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −65.9346 | −2.38699 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.5350 | 0.670134 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.1580 | 0.836189 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.9546 | −0.431095 | −0.215547 | − | 0.976493i | \(-0.569154\pi\) | ||||
−0.215547 | + | 0.976493i | \(0.569154\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.5277 | −0.919359 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.0495 | −0.864999 | −0.432499 | − | 0.901634i | \(-0.642368\pi\) | ||||
−0.432499 | + | 0.901634i | \(0.642368\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −47.1437 | −1.69345 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.1560 | −0.471968 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29.0935 | −1.04238 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0250 | 0.859682 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −68.0536 | −2.42894 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.7208 | −1.34460 | −0.672300 | − | 0.740279i | \(-0.734693\pi\) | ||||
−0.672300 | + | 0.740279i | \(0.734693\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.2098 | 0.577084 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 61.2747 | 2.17868 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −51.9961 | −1.84643 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −46.6329 | −1.65390 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.6036 | −0.729817 | −0.364908 | − | 0.931043i | \(-0.618900\pi\) | ||||
−0.364908 | + | 0.931043i | \(0.618900\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.7313 | 0.698044 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.93310 | 0.315636 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 39.0017 | 1.37634 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.2634 | 0.573208 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.0182 | 0.563867 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −45.8191 | −1.61091 | −0.805457 | − | 0.592654i | \(-0.798080\pi\) | ||||
−0.805457 | + | 0.592654i | \(0.798080\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.2866 | 1.44977 | 0.724884 | − | 0.688871i | \(-0.241893\pi\) | ||||
0.724884 | + | 0.688871i | \(0.241893\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.64736 | 0.127918 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 48.4985 | 1.69883 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −37.2360 | −1.30272 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 19.8935 | 0.695134 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 50.1840 | 1.75144 | 0.875718 | − | 0.482824i | \(-0.160389\pi\) | ||||
0.875718 | + | 0.482824i | \(0.160389\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −47.5287 | −1.65675 | −0.828374 | − | 0.560176i | \(-0.810734\pi\) | ||||
−0.828374 | + | 0.560176i | \(0.810734\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 38.2768 | 1.33263 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.5045 | −0.504370 | −0.252185 | − | 0.967679i | \(-0.581149\pi\) | ||||
−0.252185 | + | 0.967679i | \(0.581149\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.4074 | 1.26448 | 0.632240 | − | 0.774772i | \(-0.282136\pi\) | ||||
0.632240 | + | 0.774772i | \(0.282136\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.19668 | 0.284340 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 43.0779 | 1.49256 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −33.8369 | −1.17097 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.21724 | 0.145769 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.28119 | 0.182327 | 0.0911635 | − | 0.995836i | \(-0.470941\pi\) | ||||
0.0911635 | + | 0.995836i | \(0.470941\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 30.6032 | 1.05403 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 45.0790 | 1.55077 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.92779 | 0.100600 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.1893 | 0.624256 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.25376 | 0.111538 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.7810 | −1.19088 | −0.595439 | − | 0.803401i | \(-0.703022\pi\) | ||||
−0.595439 | + | 0.803401i | \(0.703022\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 30.6959 | 1.04978 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.18147 | −0.279474 | −0.139737 | − | 0.990189i | \(-0.544626\pi\) | ||||
−0.139737 | + | 0.990189i | \(0.544626\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.39184 | 0.115728 | 0.0578641 | − | 0.998324i | \(-0.481571\pi\) | ||||
0.0578641 | + | 0.998324i | \(0.481571\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.4144 | 0.525320 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.40961 | 0.150105 | 0.0750525 | − | 0.997180i | \(-0.476088\pi\) | ||||
0.0750525 | + | 0.997180i | \(0.476088\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −81.4274 | −2.76861 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.23430 | −0.143804 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.4458 | 0.591808 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −75.1647 | −2.54686 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.9323 | 0.505383 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 100.488 | 3.39712 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.5955 | 0.931835 | 0.465917 | − | 0.884828i | \(-0.345724\pi\) | ||||
0.465917 | + | 0.884828i | \(0.345724\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −25.5008 | −0.860121 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.53612 | −0.0517533 | −0.0258767 | − | 0.999665i | \(-0.508238\pi\) | ||||
−0.0258767 | + | 0.999665i | \(0.508238\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.50815 | −0.185364 | −0.0926820 | − | 0.995696i | \(-0.529544\pi\) | ||||
−0.0926820 | + | 0.995696i | \(0.529544\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.9322 | −0.636400 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.7856 | 0.597182 | 0.298591 | − | 0.954381i | \(-0.403483\pi\) | ||||
0.298591 | + | 0.954381i | \(0.403483\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −79.8407 | −2.67777 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.42405 | −0.114710 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 32.6772 | 1.09350 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28.2324 | 0.943704 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.92009 | −0.164277 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.21724 | −0.140653 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 53.4242 | 1.77982 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19.7284 | 0.656521 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −54.3363 | −1.80620 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.5259 | 0.947186 | 0.473593 | − | 0.880744i | \(-0.342957\pi\) | ||||
0.473593 | + | 0.880744i | \(0.342957\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.2354 | −0.339488 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.1530 | −1.62851 | −0.814255 | − | 0.580507i | \(-0.802854\pi\) | ||||
−0.814255 | + | 0.580507i | \(0.802854\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.63095 | 0.0539764 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 42.5080 | 1.40527 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.08110 | 0.266861 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.9059 | 1.44832 | 0.724162 | − | 0.689630i | \(-0.242227\pi\) | ||||
0.724162 | + | 0.689630i | \(0.242227\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.49238 | −0.213931 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −34.5221 | −1.13631 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36.3732 | 1.19594 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.1878 | −0.367455 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.3119 | 0.436749 | 0.218375 | − | 0.975865i | \(-0.429925\pi\) | ||||
0.218375 | + | 0.975865i | \(0.429925\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 71.3416 | 2.33813 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 31.0601 | 1.01686 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −63.4647 | −2.07552 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.2816 | −0.531896 | −0.265948 | − | 0.963987i | \(-0.585685\pi\) | ||||
−0.265948 | + | 0.963987i | \(0.585685\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.1142 | −0.689035 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.7132 | −0.577434 | −0.288717 | − | 0.957415i | \(-0.593229\pi\) | ||||
−0.288717 | + | 0.957415i | \(0.593229\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.81231 | −0.124146 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −16.2634 | −0.529047 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.9640 | 0.518761 | 0.259381 | − | 0.965775i | \(-0.416482\pi\) | ||||
0.259381 | + | 0.965775i | \(0.416482\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −56.0424 | −1.81921 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.5266 | −0.471058 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.4117 | 1.76257 | 0.881284 | − | 0.472587i | \(-0.156680\pi\) | ||||
0.881284 | + | 0.472587i | \(0.156680\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −58.8535 | −1.90446 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.42405 | 0.110684 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.5694 | −0.502763 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.2149 | −0.426288 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.6748 | 0.505114 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.7398 | −0.764211 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.88545 | 0.221421 | 0.110711 | − | 0.993853i | \(-0.464687\pi\) | ||||
0.110711 | + | 0.993853i | \(0.464687\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −35.1663 | −1.12970 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.07284 | −0.0986123 | −0.0493061 | − | 0.998784i | \(-0.515701\pi\) | ||||
−0.0493061 | + | 0.998784i | \(0.515701\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.8406 | 0.732236 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −55.0008 | −1.76143 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.3904 | 1.26021 | 0.630106 | − | 0.776509i | \(-0.283012\pi\) | ||||
0.630106 | + | 0.776509i | \(0.283012\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.5874 | −0.977577 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.3071 | −0.520645 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.5701 | 1.45346 | 0.726731 | − | 0.686922i | \(-0.241039\pi\) | ||||
0.726731 | + | 0.686922i | \(0.241039\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.4015 | 0.458871 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −17.3131 | −0.551082 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.87928 | −0.155152 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.3994 | −0.362114 | −0.181057 | − | 0.983473i | \(-0.557952\pi\) | ||||
−0.181057 | + | 0.983473i | \(0.557952\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.6417 | 0.559844 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.829222 | −0.0262881 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.4117 | 1.15317 | 0.576585 | − | 0.817037i | \(-0.304385\pi\) | ||||
0.576585 | + | 0.817037i | \(0.304385\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.25376 | −0.102944 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8004.2.a.i.1.15 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.i.1.15 | ✓ | 16 | 1.1 | even | 1 | trivial |